{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Embedded Operator Splitting (EOS) Methods\n",
    "\n",
    "This examples shows how to use the Embedded Operator Splitting (EOS) Methods described in Rein (2019). The idea is to embedded one operator splitting method inside another. The inner operator splitting method solves the Keplerian motion, whereas the outer solves the planet-planet interactions. The accuracy and speed of the EOS methods are comparable to standard Wisdom-Holman type methods. However, the main advantage of the EOS methods is that they do not require a Kepler solver. This significantly simplifies the implementation. And in certain cases this can lead to a speed-up by a factor of 2-3x."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import rebound\n",
    "%matplotlib inline\n",
    "import matplotlib.pylab as plt\n",
    "import numpy as np\n",
    "import time\n",
    "linestyles = [\"--\",\"-\",\"-.\",\":\"]\n",
    "labels = {\"LF\": \"LF\", \"LF4\": \"LF4\", \"LF6\": \"LF6\", \"LF8\": \"LF8\", \"LF4_2\": \"LF(4,2)\", \"LF8_6_4\": \"LF(8,6,4)\", \"PLF7_6_4\": \"PLF(7,6,4)\", \"PMLF4\": \"PMLF4\", \"PMLF6\": \"PMLF6\"}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first create a function to setup our initial conditions of two Jupiter-mass planets with moderate eccentricities . We also create a function to run the simulation and periodically measure the relative energy error. The function then runs the simulation again, this not only measuring the runtime. This way we don't include the time required to calculate the energy error in our run time measurements. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initial_conditions():\n",
    "    sim = rebound.Simulation()\n",
    "    sim.add(m=1)\n",
    "    sim.add(m=1e-3,a=1,e=0.05,f=0.)\n",
    "    sim.add(m=1e-3,a=1.6,e=0.05,f=1.)\n",
    "    sim.move_to_com()\n",
    "    return sim\n",
    "    \n",
    "def run(sim):\n",
    "    simc = sim.copy() # Use later for timing\n",
    "    tmax = 100.\n",
    "    \n",
    "    # First run to measure energy error\n",
    "    Emax = 0\n",
    "    E0 = sim.energy()\n",
    "    while sim.t<tmax:\n",
    "        sim.integrate(sim.t+1.23456, exact_finish_time=0)\n",
    "        E1 = sim.energy()\n",
    "        Emax = np.max([Emax,np.abs((E0-E1)/E0)])\n",
    "        \n",
    "    # Second run to measuring run time\n",
    "    start = time.time()        \n",
    "    simc.integrate(tmax,exact_finish_time=0)\n",
    "    end = time.time()\n",
    "\n",
    "    return [Emax, end-start]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Standard methods**\n",
    "\n",
    "Let us first run a few standard methods. WH is the Wisdom-Holman method, WHC is the Wisdom-Holman method with symplectic correctors, and SABA(8,6,4) is a high order variant of the WH method. All methods except the LEAPFROG method use a Kepler solver. We run each method for 20 different timesteps, ranging from $10^{-4}$ to $0.3$ orbital periods of the innermost planet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/rein/git/rebound/rebound/simulation.py:675: RuntimeWarning: WHFast convergence issue. Timestep is larger than at least one orbital period.\n",
      "  warnings.warn(msg[1:], RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "dts = 2.*np.pi*np.logspace(-4,-0.5,20)\n",
    "methods = [\"LEAPFROG\", \"WH\", \"WHC\", \"SABA(8,6,4)\"]                        \n",
    "results = np.zeros((len(dts), len(methods), 2))\n",
    "for i, dt in enumerate(dts):\n",
    "    for m, method in enumerate(methods):\n",
    "        sim = initial_conditions()\n",
    "        sim.dt = dt\n",
    "        sim.integrator = method\n",
    "        sim.ri_whfast.safe_mode = 0\n",
    "        sim.ri_saba.safe_mode = 0\n",
    "        results[i,m] = run(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then plot the relative energy error as a function of the timestep on the left panel, and the relative energy error as a function of the run time on the right panel. In the right panel, methods further to the bottom left are more efficient. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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NwpAhQzBjxgwEBAS813utW7cOarUac+fORXh4OH788UcAwP79+9GiRQscO3ZME5EFoeDIqevJkA597kYXCo6bN2/y22+/pbW1tXyb4n1vfRiCa9eusUOHDgRAGxsb+vj4sF+/fgTA8ePH6+R7BHFLTpaWlsZ27drRxMSEu3fvfqf3UKvVrFatGps0afKfr23fvp12dnYEwE8++YQnT55838iCoDdya0tED5Mg5MHs2bNRrVo1+Pr6onXr1jh8+DAuXLhg1Lclbt++jb59+6JWrVo4ceIEZsyYgVu3biEoKAhr167F1KlT8fPPPxv190gJKpUKmzdvRp06ddCjRw9cuHAh3+9x8eJF3Lx5EwMGDPjP1zp16oTbt29jwYIFCAsLQ6tWrdC/f38NJBcEPZdTJWVIR0H4VCjol8uXL3PEiBEMDg6WH8+ZM4cPHz5UOJmy1Go1L1y4wCFDhlClUrFQoUIcN24cHz9+zJcvX7JLly4EwF9++UWnuSB6mP7jwYMHdHR0pI2NDa9du5av1w4fPpwWFhZ88uRJrs9LTk7m/PnzuWbNGpKZkx/OnTv3zpkFQWm5tSWKFzO6OApSIyco5+HDh5w/fz5r1qxJADQ3N2dAQIDSsfRCTEwM58yZI896s7Cw4PDhwxkTE0OSfPHiBd3c3AiAPj4+Os8nCqY3CwsLY9myZWlpaUk/P7883x798ccf6enpme/rBQQEEABdXFx45MgRcctaKHBEwVTAGjlB99LT01m6dGkCYIMGDejr68v4+HilYynqxYsX3LJlizweBgCbNGlCf3////Q8eHp6EgD9/PwUySoKppw9ePCAbdu2JQB27NhRqz/XSUlJnDt3Lm1tbQmAjRo1YmBgoCichAJDFEwFsJETtEetVvPSpUscOXIkmzRpIjfm27dv5/Xr1xVOpyy1Ws1z587Rw8ODxYsXJwDa29tzwoQJDAsLy/F1MTEx3LRpkw6T/psomHKXkZHBefPm0czMjHZ2djxx4kSOzw0JCWFGRsZ7Xe/FixdcvHgxK1SoICZHCAWKKJgKaCMnaFZcXNx/brl1796dT58+VTqa4qKjozlr1ixWqVKFAGhpack+ffrw0KFDTE9Pf+Nrnj17xqlTpzItLU3Haf9LFEx5c/HiRTo7O1OSJE6aNOk//989fPiQKpWK06dP18j1UlNTGRkZSZJ8/Pgx69Wrx+XLl/Ply5caeX9B0DRRMBXwRk54d8nJyXz27BlJctu2bfJtAj8/Pz5+/FjhdMq7d+8ePTw8aGZmRgBs1qwZly5dmqcict26dVSpVDxz5owOkuZOFEx5l5SUxAEDBhAAGzZsyJs3b8pfS05O5tq1a/nXX39p/LrXr19nnTp15F7LuXPnyr+bgqAvRMFkAI2ckHcZGRk8evQoBw4cSCsrK06bNo0kmZKS8q8/DsYse6FkZmbGr7/+Os/blvzzzz/yf2vjD+u7EAVT/m3evJklS5akhYUFvb29c+xJ1CS1Ws19+/axVatWBMDixYvz0aNHWr+uIOSVKJgMqJETcjdp0iTa29sTAK2srDho0CCePXtW6Vh6402FUtYtk7dRq9VcvXo1S5Uqle9p6tomCqZ3ExsbKy862rRpUx46dIienp46uWUWFBT0r+UnFi9ezJCQEK1fVxByIwomA2vkhP8XHR3N9evXy4+7dOlCNzc3btq0icnJyQom0y/37t2jp6cnzc3N810okWRCQgJ79OhBAGzZsmW+XqsLomB6d2q1mmvXrmXx4sVpbm5OAFy0aJFOMzx9+pTFihUjALq6uvLYsWNioLigCIMrmAB8AuAPAEsAfPK25xtiI2fM/vnnH65bt46ff/65PN09OjqaJN97do+hed9CiSRPnDjB8uXLU6VScebMmTq5dZNfomB6f9HR0XR1dZXX2dL17ev4+HhOnz5dXt6jfv36vHz5sk4zCEJubYnOt0aRJGmFJElxkiRdf+18W0mSwiVJui1J0ri3vA0BPAdgCSBKW1kF/XPs2DHY2tqib9+++OuvvzBx4kSEh4ejXLlyAAATE7HbDwDcu3cPw4cPR8WKFbF06VIMHDgQf/31FxYvXgwHB4c8vUdaWhomTpwIFxcXWFpa4syZMxg/frzYSNdAlStXDnv37sWYMWPw8uVL1K5dG4sXL4ZardbJ9UuWLIlJkybh7t278Pf3R0pKCmxsbAAAf//9N54/f66THIKQo5wqKW0dAFoCqAvgerZzpgDuAHACYA7gKoBqAGoA2PPaURqAyavXlQGw/m3XNORPhYYua7r7jh07SJKPHj1i//79efz4cdGb9JqnT59y+fLldHFxoSRJNDMz41dffcW7d+/m+71u3brF+vXrEwAHDx7MpKQkLSTWHIgeJo1Rq9Vs1KgRLSws5J6e3NZt0maOLC4uLixRogQnTJjA2NhYnWcRjEdubYnOC6bMPKjwWsHUBMDBbI/HAxifh/cxB7Dtbc8zhkbOkKSkpHDr1q3/WmF6xIgRSsfSSykpKdyxYwe7dOki/4FzdnbmlClT3nmc0YsXL1i2bFmWKFGC27Zt03Di3KnV6ncauyIKJs06fvw4AbBPnz7yJAp3d3feuHFDkTxnzpxh586dKUkSzc3NOXjwYIaGhiqSRTBsBaFg6gpgWbbH/QD45vL6zgD8AWxGDmOYAAwDEAwg2MHBQdPfU0GLPvvsMwKgnZ0dJ0yYwPDwcKUj6ZWMjAyePHmSQ4cOlVfjLl26NEeOHMmgoKB3Hiz77Nkz+bUHDhzg/fv3NRn7rWJjY9m4cWNu3bo136/VZsFkrG2Ji4sLy5Qpw/j4eP7yyy+0srKiJEmsUaMGHzx4oEimW7du8euvv6alpSXnzp1LMvP3QQwQFzTF4Aqm/B7G8qmwIIqLi6OPjw8bNWokL5Z48OBBHjhwQC8HFyspJCSEP/zwAx0cHAiARYoUYd++fbl///73Xm377t27tLOzo7+/v4bS5l3WrdX09HR+8cUX79SrJXqYNO/UqVMEIBcmDx48YK1atWhiYsKiRYty+vTp/1qTS5fi4uLk28SrV69m06ZNuWfPHlE4Ce+tIBRM73RLLq+HMTVyBUFqaip37tzJjh07UqVSyRveKtXdr6/UajWvXLnCyZMns3r16gRAU1NTurq6cv369Xz+/LnGrpWRkcGvv/6aFy9e1Nh75sWaNWtYu3Ztvnjx4r3eRxRM2uHi4kInJ6d/nQsPD2enTp3k7YW+/fZbnfdGZrd582b5Q0StWrW4efNm8WFLeGcFoWBSAYgA4Jht0Hd1TV3P2Bo5fZX1R/HGjRsEwDJlyvC7774z+g1vs8vIyODZs2f5/fff86OPPiIASpLEli1bcsGCBXz48KHGr6nEp/KsXqUjR46wffv27/3vEgWTdoSFhfHvv/9+49cmT57MIkWKyIV8x44defDgQUUmY6SmpnLVqlWsXLkyAbBjx446zyAYBr0qmABsBBALIA2ZSwIMfnW+HYBbr2bLTdTkNY2tkdMnjx8/pq+vL+vVq8eePXvK548fP87U1FQFk+mPtLQ0Hjt2jCNGjKCdnR0BUKVSsU2bNgwICNDqeJGoqCg6Ozvz2LFjWrtGdsnJyXR1deWcOXM0+r6iYFJGWloaIyIiOHbsWFpaWhIAK1asyLlz5yqyV2N6ejq3bt3K/fv3k8wcl7dw4ULFbh0KBY9eFUxKHKKR072jR4+yW7du8srBtWvX5pIlS5SOpTdevnzJvXv3cvDgwSxVqhQB0NLSkh07duTatWv55MkTneTw8vKiSqXinTt3tHqd7L0Offr0oZ+fn0bfXxRM2rNkyRJu3rw51+dERETQ1taWw4YNY7NmzeSf5/79+/P8+fM6Svpfq1evJgDa2Nhw2rRpjIuLUyyLUDCIgskIGzldU6vVPH/+vDz4eNy4cSxVqhRHjhwpVut9Ra1W89y5c/T09KS1tbW8313v3r25bds2jY5JyouoqChaWFhw8ODBWr1OZGQkq1SpopXbiVlEwaQ99evXZ+fOnd/6vOyzLI8ePcphw4axaNGiBMBmzZopNij71KlT8grmlpaWHDp06HtPkhAMlyiYjLCR05WIiAhOmzaNlSpVIgDu27ePZGbjKW65ZYqMjOTPP/8sj6+wtLRkr169uGfPHqakpCiWa8SIEVSpVIyIiNDqdc6ePcuPP/5Yq4P6RcGkPdkLobw4fPgwAfDYsWNMTEzkggUL5EHZNWrU4Lp16xQpWG7cuMFhw4bRzc1NPnf16lUxs074F1EwGWEjp22xsbFy1zsAfvLJJ1y+fLm8NICxS0xM5MqVK+ni4iJ/j1q1aqU336OoqCiam5tzyJAhOrmetv8oiYJJfzx+/Jg+Pj7/Wjg1NTWVa9asYbVq1QiAFSpUoK+vryIbZGf9LN6/f58qlYrVqlVjQECA2KxbICkKJtHIaUDWUgCrVq0imTkmpXXr1pw5c6be7VyvlPT0dB48eJB9+vRhoUKF5FW3p0+fnuNMI6Vk9S5pO9fevXt10psgCibtSUpKYu/evd86jikvMjIyuGvXLjZu3FgeW/Tzzz/rbMxedi9fvpSXtQDAUqVKcdKkSYoMVhf0hyiYjLCR05SQkBCOHj1a3kG8Vq1aogv7NWFhYfzhhx9oa2tLACxRogQ9PDx49uxZvfxe3b9/n+bm5hw6dKhWrxMUFEQAGh/g/SaiYNIetVrNUqVKceDAgXl+TVJSEs+ePZvre548eVIeW2RlZcXx48crUqyo1WoeP36c7u7uNDc3l/de1MffXUH7RMFkhI2cJvz444/yFPdOnTpx9+7dYrDkK4mJiVy2bBmbNm0qr0Pj7u7O33//XdFxSXkxfPhwnfQuqdVq7tq1Sye3OkTBpF3t27dntWrV8vz8OXPmEAAfPXr01udeuXKF3bt3JwAWK1aM06ZNY2Ji4vvEfWfZJya4u7tz6NChvH37tiJZBGWIgslIG7n8SE9P56FDh9izZ09evXqVJHnu3Dn6+PiIqbivqNVqnjp1igMGDGDhwoUJgFWrVqW3t3eB2UE9PT2dDRo00Hrvkq6Jgkm7pk+fTgB5vnV2584d7tmzJ1/F8tWrV9mhQwf59tjcuXMVG1eUlpZGDw8PWlhY0MTEhH369BE7ERgJUTAZaSOXF7dv3+akSZNYvnx5+XaSrneo13dRUVH8+eefWbFiRfn2wdChQ/X2ltvbZGRkyPtwaUNqaipbtmypkTEveSUKJu3Kmvl26NAhrV/r/Pnz/PzzzwmA5cqVo5+fH1++fKn1675JTEwMx4wZI39A2rJliyI5BN3JrS0xgWB01Go1ACAlJQW1a9fGzz//jOrVq2Pz5s2IiYlBly5dFE6ovJcvX2Lbtm1o164dHBwcMHHiRNjb22P16tWIjY1FQEAAGjduDEmSlI6aZ/Hx8Xj69ClMTExQtGhRrV4HAAoVKqS1awi61aBBA0iShHPnzuX5NWFhYTh06FC+r9WwYUMcOnQIJ06cgKOjIzw9PVG5cmWsWrUK6enp+X6/92Fra4u5c+ciMjISP/30Ez7//HMAwPHjx3HkyJHMXgfBeORUSRnSYayfCrNLS0vj/v372atXLzZq1Eg+HxgYqOjGmfpErVbzzJkz/Prrr1miRAkCoL29PSdNmmQQ4xg8PT1ZunRpnWwToVarddr7BtHDpHXVq1dnu3bt8vz8Pn360M7O7r2uqVaruX//ftarV48A6OjoSF9fX8W3OmnTpo28g8G6devEmnMGJLe2RPFiRheHMTdy4eHhHDNmDMuWLSvfcvP09NT7gcm6dOfOHU6dOlW+5VaoUCH27t2bBw4cMKhdzy9dukR/f3+tXuP48eOKrDMlCibtGzx4MK2trfNcCIeFhfHWrVsaKZyzJhA0adJEHuM0bdo0xZYASElJ4fLly1m1alUCYPny5blu3TpFsgiaJQomI2vkHjx4IA/OXLNmDVUqFTt06MDt27eLQumVJ0+eMCAggC1atCAASpJEFxcXrly5UrEZOgVdUlISixUrxn79+un82qJg0r6lS5cSAG/duqVYhqyJF+3btycAFilShKNGjeK9e/cUyZORkcE9e/bIi9KSmb8HUVFRiuQR3p8omIygkUtJSeGWLVvYvn17mpqacu7cuSQzd4fPy0OmzysAACAASURBVNReY5Camso9e/awe/futLCwIABWqVLF4BffvHfvHvv376+TPyoXL17kX3/9pfXrvE4UTNp348YNuri48NKlS3l+ze+//86DBw9qJU9ISAj79etHlUpFlUrFL7/8ktevX9fKtfIiqyfNx8eHZmZm7N+/v6J5hHcjCiYDbuQyMjL4zTffyJu52tnZcdy4cQwPD1c6ml5Qq9UMDg7myJEj5cU3S5YsSS8vLwYFBRXIWW759fXXX9PMzEyrRaHS30dRMOmnGjVqsH379lq9RmRkJL/55ht5JpubmxvPnDmj1WvmJiIigl5eXnIed3d3RfMI+fNeBRMAUwDfvu15ujwAtACwBMAyAGfe9nxDa+QePXrEHTt2yI/d3NzYs2dPHjx40KDG3LyPyMhIzpw5Ux5jYG5uzi5dunDXrl2KTVFWQmRkJM3MzOjh4aHV6wwePJiTJ0/W6jVyIwom3cnPbf27d+/qbBhAfHw8p06dypIlS8p7Nx44cECxYv7Ro0f86aefaG1tzZYtWyqSQci/9+5hAhCUl+fl8b1WAIgDcP21820BhAO4DWBcHt+rI4Cv3vY8Q2jk0tLSuHv3bnbu3JlmZmY0MTGRV6VV+tO9vnj27BmXL1/OTz75RN7wtnnz5vT392dCQoLS8RTx1Vdf0czMTKu34zIyMjhgwABOnDhRa9d4G1Ew6caCBQtoaWmp+Cy13Dx//pw+Pj60s7MjANatW5dbt25V7MPk8+fPGRERQTJzXaeGDRty/fr1YtcEPaWJgskHgO+rnp26WUdeXvuG92r56vXXs50zBXAHgBMAcwBXAVQDUAPAnteO0tletwWA1duuWdAbuWPHjsmz3GxsbDh69Gheu3ZN6Vh6IS0tjXv37mWPHj1oaWlJAKxYsSKnTZvGO3fuKB1PUXfv3tVJ71IWJQt3UTDpxpkzZzhhwoQ8fwBJTEzkjBkzePr0aS0n+6+UlBQuW7aMzs7OBMBKlSpx+fLlivYwX7hwQe71dnR05KJFixRbzVx4M00UTMffcBzLy2tzeL8KrxVMTQAczPZ4PIDxb3kPBwBL83K9gtbIJSQk0M/PT15VNyoqih06dOCOHTvEeh+vXLt2jd988408Lsna2pqenp4FdvVtbRg2bBjNzc212rt05coV+dOzkkTBpJ9SUlJobm7OWbNmKZYhPT2dmzdvZu3ateW11RYsWKDYjOGMjAzu3LmTjRs3JgCWLVuWz58/VySL8F96N+j7DQVTVwDLsj3uB8D3Le8xFUDTXL4+DEAwgGAHBwfNfke1IKunpFu3bjQ3NycAfvXVV0rH0itJSUlctmwZGzVq9K9xSTt37jSqcUl5cffuXapUKnp6emr1Os2bN6ezszMzMjK0ep230WbBVNDaEm17/vx5vvZV0+Y2PPmhVqu5b98+Nm/enAD44YcfcvXq1YrdqlOr1Txx4gRnz54tn/Pz8zP6nnGlaaKH6QMA87MaDQDzAHyQl9fm8H7vXTDl5ygInwpdXFzkGVwjR47kpUuXRE8JMxuVoKAgDh06lEWLFiUAVqtWjT4+PmK5hBw8ffqUnTp1orm5udZXcY+KiuKff/6p1Wvkhehh0p1evXrR1ta2wH5IUavVPHjwIOvWrUsArF69Onfu3Kl4e/vgwQN5s99u3brx/PnziuYxVpoomH5/1aPj9Or4CcD2vLw2h/d771ty+Tn0rZGLj4/nwoUL2apVK3nw5I4dO7hjx44C2whp2pMnT+jr68tatWrJq28PGDCAp0+fVrxh01dZn+QfPnxICwsLrc5a07f/D0TBpDtbt24lALZu3TpPq7rfvHmT/fv314tbt9llZGRw8+bN8hinxo0b88SJE4pmio6O5rhx4/jBBx8QAFu2bMnQ0FBFMxkbTRRMV/JyLq/HGwomFYAIAI7ZBn1Xf9f3f/3Qh0YuLS2NgYGB8iw3vNqHKCwsTOloeiNrFd9+/frJA7jr1q3LxYsXK7LdRkHSu3dvNm/eXH4cGxur1estWrSI3bp105vZUqJg0q2VK1dSpVKxRo0ab+3FvHr1KsuUKcPjx4/rJlw+paamMiAggOXKlSMAtm3bNl+Lc2pDYmIifXx8WLVqVcbHx5Mkb9++LQaI64AmCqazAJpne9wMwNm8vPYN77URQCyANABRAAa/Ot8OwC1kzpab+C7vndOhZCOX1WMUHBwsz3L79ttveeXKFcUy6ZuoqCjOmjWLlStXJgBaWVnx66+/5sWLF5WOprdiY2M5c+ZMvnjxgmTmFjg+Pj46G0s0f/58urm56U1PkyiYdO/w4cO0srKinZ1dru2ZrjdiflfJycn09vaWN97u2rWr4m1Q1vdNrVazQYMGLFmyJCdOnMjo6GhFcxkyTRRMtV71+tx9dVwGUDMvr9WHQ9eNXEJCAhctWsQGDRpw0KBBJP//vrmY5ZbpxYsX3LRpE9u2bUsTExMCYLNmzbhy5UoxYyQHarWaZ8+eZe/eveVeSm1tO5GT7L0J+vRHUBRMyrh69Srt7OxoZWX11p/Fly9fcvv27TpK9u6ePHnCSZMmybfFvvjiC544cULRn/esAeIdO3akJElUqVTs06eP+OCtBe9VMAEwAdD91X8XA1Dsba/Rt0NXjdyxY8f+tU9ZzZo1uWTJEp1cuyBQq9U8f/48PTw8WLx4cXmX70mTJimy/1hBkZqayrVr17J+/foEwGLFivGbb77R+SaoixYtYpEiRfTyNrIomJRz//591qxZkyqViv7+/jk+b/78+QTAy5cv6zDdu3v69Cl/+eUXeemSJk2aMDAwUPEZoXfu3OGoUaNoZWUlf79fvnwpFsLUEE30MOmkMdLWoc1G7tatW/Iv0MiRI2ltbU0vLy9evHhRrz6BKykmJoazZ8+WF2yztLRknz59ePjwYcUbH3329OlTent7097eXt4o2NfXl4mJiYrkiYmJ4cSJE/Wyl1QUTMp69uwZ27RpwxEjRuT4nNTUVO7fv1+HqTQjOTmZixYt4ocffkgA/Pjjj7lu3TrFC5Rnz57Jt+R9fX3p4ODAOXPmGO2uBpqiiYJpFoDvAJQHYJ115OW1+nBoupF7+vQp/f392bRpUwKQZ1YkJCQothiavnnx4gW3bNnCdu3aybfcmjZtyqVLl4oB3HmUtdSEi4sL9+7dq0hxeebMGX777bd6X/yLgkl5GRkZcvt37tw5btiwIcefm5CQEAYGBuoy3ntLTU3lmjVrWK1aNXmlbj8/P72Y+HDkyBF5S6giRYpw1KhRWt1s25BpomD6+w1HRF5eqw+Hphq5uLg49urVS57BVbVqVc6ePVve083YZWRk8OTJkxwyZIh8/9/e3p4TJkxgeHi40vH03u3btzlgwAA+fvyYJHn69GleuHBB0UwzZsygk5MT4+LiFM3xNqJg0i99+/alg4NDjsWEm5sbK1SoUCA/YGat1N2wYUN57bxJkyZpfWZqXly+fJl9+/alqamp2PD3HWliDFOztz1Pn4/3aeRCQ0PlLUpSU1NZuXJlenp6MigoSO8/detKWFgYJ06cKHdZFylShF9++SUPHz6s2Cq6BYVarZZvsV27do1FixaVf96UkpycLI8py8jIKBA9gqJg0i9paWnyitUpKSnct2/fv77+5MkTvVuXKb+yBmJ36NCBkiTR3Nyc/fv314uB2Hfv3pVzPHz4kB06dFB84HpBoYkepst5eZ6+Hvlt5BISErh48WJ5rx8nJ6d/Te8UMnvbFixYwAYNGhAATUxM2KZNG65bt07McsuDlJQUrlq1ih9//DF79eoln9eH7527uzudnJwK1Kd/UTDpr19//ZUA2KdPH7n3NDsfHx/Fp++/r7/++osjRoxg4cKFCYCfffaZYrfRX3fixAl54HrDhg25bds28UE2F5oomOYC6AJAysvz9e3ITyPn4+Mjz3KrXr06vb29GRMTk+fXG7IXL15w8+bNdHNzo0qlkhffnDdvnvge5cGLFy8YGBjIfv36ybcsP/74Y65du1bpaP9y/vx57t69W+kY+SIKJv2VmprKKVOmUKVS8YMPPuCECRPkYQxPnz6lg4MDPTw8FE6pGQkJCZw9ezbt7OwIgJUrV+aSJUsUH+eUnJzMJUuWsGLFigTASpUqKZ5JX2miYEoCkAEgFUDiq8eJeXmtPhz5aeQOHTrEESNGMDg4WPQmMbNH7Y8//uDQoUPlP/J2dnYcO3YsQ0JClI6n9168eMGdO3eyT58+tLKyIgAWL16cAwYM4KFDh/TmZ2zu3Ln09vZWOsY7EwWT/rty5Qq7dOlCSZJoaWlJT09PRkREMDo62uB6PFJTU7l+/XrWq1dPHuc0efJkxccCpqenc9u2bZwwYYKiOfSZJgomE2RuiDv51WMHAI3y8lp9OEQjl3+3b9/mTz/9RCcnJzEuKZ+Sk5Pl21ne3t4EQGtraw4aNIj79+/Xu/0C09LS2LlzZ3bt2lVvCrj8EgVTwREWFsbBgwfTzMyMpqam7N27N8PCwhgaGsq9e/cqHU+j1Go1T548SXd3d3lJFQ8PD7HunB7TRMG0GMAiAKGvHpcAcCEvr9WHQzRyefPkyRP6+/uzWbNmBEBJkti6dWuuWbNGL8bWFARhYWEsWrQoN2zYQDJzM80DBw7o5dpFryuoxRIpCqaCKCoqimPGjGHRokV5/PhxdunShba2tgb7gSw0NJRDhgyhubk5JUlily5deO7cOaVjCa/RRMF06dX/Xs527mpeXqsPh2jkcpaamso9e/b8a4XyqlWrctasWW/dVNPYpaen88iRIxwwYAAnTZpEMnNW2ejRoxXfvDOvkpKSDGJZDFEwFVxPnz6lWq3mrVu3OGjQIDZs2NBgiyYycwHY8ePHy7sdtGjRQi9WEBcy5daWmCBv0iRJMgVAAJAkyQaAOo+vFfQMSQQHB2PUqFGwt7eHm5sbjh07hq+++grBwcG4ceMGfvjhB9jb2ysdVe+QxJUrV/Ddd9/BwcEBrVu3xvbt25GamgoAMDExwbx581CnTh2Fk+bN8uXL4eDggHv37ikdRTBSH3zwASRJgrOzM1q1agVXV1eYmpoCAGbPno3Lly8rnFCzbG1tMXPmTNy7dw8+Pj6IjIyEu7s7qlevjoCAACQnJysdUchJTpVU9gNAHwCBAKIA/AwgHEC3vLxWHw7xqTDTnTt3OG3aNFauXJkAaG5uzs6dO3PXrl0F4paRku7evcuZM2fKq/yamZmxQ4cO3LJlC5OTk5WO987Cw8M5Z84cpWO8N4geJoNw6dIlDhw4kCkpKYyJiWGhQoXk6fArVqwwyJldWQPE69SpI493HD9+vOjhV0hubUmeGwoAVQAMBzACQNW8vk4fDmNu5OLj4+nn5ydv4wKArVq14tKlS8WeQ3mUtY4MADZv3pyLFy9mfHy80rGEbETBZBgOHDjAEiVKyBv0JiQk8LfffpP3ofzggw84cuRI3rhxQ+Gkmpc1QLxz5840MTGhSqViz549xTgnHdNIwVSQD2Nr5JKTk7l582a6u7vL6yVVr16ds2bNEvsL5cH9+/fZpUsXnjp1iiR59epVzpgxo8CvTPy6+fPnMzQ0VOkYGiEKJsOQnp7+xlmkWcVEr169aGZmRgDs1KmTwa7/FhERwdGjR7NYsWIEwMaNG3PTpk3iToAOGFzBBKAagC3InL3X9W3PN4ZGLqtBGThwoLzeT7ly5fjdd9/xypUrBXoGlC6EhITw+PHjJDNX2/7oo4+4adMmZUNpUUxMDC0sLPjLL78oHUUjRMFkeHJqsx4+fMhp06bR0tKSH374oUEXEYmJiVy4cKG84KSdnR1/+eUXeTslQfP0qmACsAJAHIDrr51v+2ps1G0A497yHmMAtHj134Fvu6YhN3Lx8fGcP38+q1SpQgC0srLiwIEDeeTIEYOeaaIJ8fHxXLhwoby4XO3ateWvGUOBGRcXx2fPnikdQyNEwWQ4Hjx4wIYNG3LdunW5Pu/WrVsMDAwkmfn7qg+b32pLRkYGd+/ezdatWxMAS5Uqxfnz5/PFixdKRzM4ubUleZ0lp0mrXhVHslcz8BYBcEVm71EvSZKqSZJUQ5KkPa8dpQGsBdBTkiRvACV1nF9xJPHHH3+gb9++sLOzw+jRo1G8eHGsXLkSDx48wIoVK/DZZ5/JM02E/5eWlobdu3eja9eusLW1hZeXF9RqNX777TccOnRIfp4kSQqm1K7MNgGwsbFBsWLFFE4jCP9mY2ODUqVKoVChQrk+z9nZGf/73/8AACtWrEClSpVw8+ZNXUTUORMTE7i5ueHw4cMICgpCnTp1MHr0aDg7O2PZsmVIT09XOqJxyKmS0uYBoAKy9TABaALgYLbH4wGMz8P7mALYlcPXhgEIBhDs4OCgyQJUMY8fP+avv/4qD4AsVqwYhw8fzqtXryodTe/duXOHo0ePljehLF26NEePHm2U37vZs2ezQ4cOerfi+PuAFnuYDLEtMTQRERH84Ycf5LWMnj59qnAi7Tt27Ji8QbyzszM3btwo1nLSgNzaEiV6mN7EDsD9bI+jXp17I0mSKkiSFABgDQDvNz2HZADJ+iTr29jYaDSsLpHE6dOn8eWXX8LOzg6jRo1CsWLFsHz5csTExMDX1xc1a9ZUOqZeSk5OxtOnTwEA169fx8KFC9G8eXMEBgYiKioK8+bNM8rvnYWFBQoVKgRzc3OloxQIhtKWFDTp6emIiYnJ03MdHR0xa9YsmJiYIC4uDhUqVMCQIUMQFRWl5ZTKcXFxwZkzZxAYGAhLS0v06tULdevWxd69e+VeZEHDcqqktHngvz1MXQEsy/a4HwBfTV2vII47iIuLo4+PD6tXry6PTfLw8JCn2wq5S0xMpLW1NSdOnEgyc780Q1jRWngziDFMBqdFixZs1apVvl+XkJDAUaNG0dzcnBYWFvzuu+/4+PFjzQfUIxkZGVy/fj0/+ugjAmDTpk3F6uHvKLe2RF96mKIBlM/22P7VOaOSlpaGwMBAdOrUCeXKlcO3336LwoULY9myZYiJiYGfnx9q166tdEy9lJSUhKVLl2LMmDEAACsrK4wfPx7t27cHAKhUKpQuXVrJiHrh6tWr4tOnUCCMHDkS33zzTb5fV6JECfj4+ODWrVvo2bMn5s2bBycnJ8ycORP//POPFpIqz8TEBL1790ZoaCj8/f1x//59uLu7o3Llyli4cCGSkpKUjmgYcqqktHngvz1MKgARABwBmAO4CqC6pq6n758KQ0JC/jO+ZsyYMQwJCVE6ml5Tq9UMCgri0KFDWbRoUQJgzZo1xcyRHAQFBREA16xZo3QUjYPoYRJyEBISQnd3dwJg2bJl6efnZ9BLEZCZq4dv3ryZTZo0kce7jh492uDWktOG3NoSJYqljQBiAaQhc6zS4Ffn2wG4BeAOgImavKY+NnKPHz+mr6+vPKVdpVKxU6dODAwMNPhf5veVkJDAhQsXsnbt2gTAQoUKceDAgTxz5oxRLAfwrpKSkujn52cwSwlkJwomw/To0SONrYf2559/snnz5gTAwYMHa+Q9C4Jz586xV69eVKlUNDExYefOnXnq1CnRVuZArwomJQ59aeTS0tK4b98+duvWjebm5gTAWrVq8ddff2VcXJzS8fReZGQke/bsSQsLCwJgnTp16OfnZxQzYoTciYLJMM2dO5cAeOfOHY28n1qt5u7du3nt2jWS5N9//809e/YYRfFw//59jh8/ntbW1gTAunXrcs2aNQY1W1YTRMGkYCOnVqt5+vRpjhgxQr7lVrJkSY4cOVIM4M6De/fuMTg4mGRmz1K5cuU4YsQIXrp0SeFkBcuqVav4+++/Kx1Da0TBZJji4uK0ulPBt99+S0tLSz548EAr76+P/vnnHy5ZskRe7LhcuXKcPXu2+OD5Sm5tiZT5dcNWv359BgcH6+x6JHHt2jVs3LgRmzZtQmRkJCwtLeHm5oZevXqhffv2sLCw0FmegoakvHBk7dq1YWFhgfPnzwMAMjIyxIKc+UQSTZs2RalSpbB7926l42iFJEkXSdbX9nV03ZYI2pWamoqLFy+iSZMmIImJEyeiW7duqFOnjtLRtE6tVuPQoUOYO3cujh49CisrK3z11Vf45ptvYG9vr3Q8xeTaluRUSRnSoatPhX/99RenTZsmLyxpampKV1dXrlmzxiDHjWja9evXOWrUKDo6OjIpKYkkeebMGTFQUQPS09P56NEjpWNoDUQPk8F68OCBTibBREZGskSJEgTAHj168NatW1q9nj65ePEie/bsSRMTE6pUKn755ZfybUtjk1tbongxo4tDm41cVFQU582bx/r16xMAAbBFixZcvHixQf+B0qRr166xU6dOBEAzMzN27dqV9+7dUzqWQVCr1UaxFosomAzXo0ePWLhwYa5cuVLr13ry5AknTpzIwoUL08zMjFOmTGFKSorWr6svIiIi6OXlxcKFCxMAXV1deezYMaMY45VFFEwabuQSExO5atUqfvbZZ5QkSR5A5+3tLf7Q58ONGzfYvXt3edrrTz/9JAa/a9jJkyfp7OzM69evKx1Fq0TBZNieP3+u0+vFxsayd+/eBMBq1arxzJkzOr2+0uLj4zl9+nTa2NjIE2xWr15tFMWjKJg00Milp6fz4MGD7Nu3r1x9Ozk5cfLkyQwLC3vv9zcmYWFh7N27NyVJYtGiRTlx4kSDX4lXKX/88QfbtGnDf/75R+koWiUKJkEb9u7dy/Lly1OSJHp5eTExMVHpSDqVnJxMf39/eZhJmTJlOGXKFIMeJC8Kpvdo5K5du8bvvvuO5cqVIwAWL16cw4YN459//mlU3ZSa9Omnn7Jw4cL84YcfxG1LQSNEwWTY1Go1e/XqxTFjxuj82omJifTy8qIkSZw3b57Or68P1Go1Dx48SFdXVwKgubk5BwwYYJAzvXNrS/RlaxS98uDBA8yfPx+1a9dGzZo18euvv6J+/frYunUrYmNj4e/vj2bNmskzuYTcxcTEYNiwYYiOztztZvHixfj7778xa9YslCpVSuF0huv8+fNITk5WOoYgvDdJklCyZEkUL15c59e2srLCggULEBQUhBEjRgDI/N169OiRzrMoRZIkfPHFF9i3bx/CwsIwZMgQbNmyBXXq1MEnn3yCnTt3IiMjQ+mY2pdTJWVIR14/FYaGhrJt27Y0MTEhADZo0IALFy4U42reUdaK5REREbSysuLWrVsVTmQ8/vnnHxYvXpwDBgxQOopOQPQwCTqSlpbGChUq8NNPP1U6iqISEhLo7e1NBwcHAqCjoyPXrl2rdKz3lltbolK2XNMvxYsXR3h4OMaNG4d+/fqhSpUqSkcqcMLCwrBz507s2rULVlZWOHToEBwdHREdHQ0rKyul4xmNQoUKYdeuXbC2tlY6iiBoVGxsLGxtbRW7vkqlwp49e+QelcjISGzatAn9+/dH2bJlFculayVKlMB3332HUaNGYdeuXfj111+RmJiodCytEgtXvoakuNWWD2q1GkFBQdi5cyd27tyJ8PBwAED9+vXRtWtX/PDDDwonFIyBWLjSOEyYMAGLFi3Cw4cPYWlpqXQcAEBAQAC++uorqFQq/O9//8OQIUPQpk0bo1xgV61Ww8SkYI/0ya0tET1MrxHFUt4EBwdj6dKlCAwMxIMHD6BSqeDi4gIvLy+4u7ujfPnySkc0Wjt27MC1a9cwbtw4saK8YFA6dOgAe3t7qNVqpaPIhg0bhpYtW2LFihVYtWoVduzYATs7OwwaNAiDBg1ChQoVlI6oMwW9WHobw/7XCRqTlpaGbdu24cGDBwCAq1evYsOGDWjZsiXWr1+PR48e4dChQxg+fLgolhR2+vRp/P777zAzM1M6iiBoVKNGjeDp6YnChQsrHeVfqlSpgjlz5iAqKgq///47atasiRkzZsDJyQlffPEFdu3apXREQQPELTkhV1m3KK9du4ZatWohICAAQ4cOxYsXL2BiYiJ6MPRUcnKy3v1R0SZxS854vHz5Evv27YOLi4sis+by6t69e1i1ahWWL1+OVq1aYc2aNUpHEvIgt7ZE73uYJElykiRpuSRJ23I7J2gOSZw7dw59+vTBkCFDAAA1a9bEqVOnMGjQIACZg4pFsaRf1Go1Hj58CABGVSwJxuX69evo3LkzduzYoXSUXDk4OGDy5MmIiIjAwoULAQBXrlyBi4sLIiIiFE4nvAutFkySJK2QJClOkqTrr51vK0lSuCRJtyVJGpfbe5CMIDn4beeE95eSkoLVq1ejQYMGaNKkCXbv3v2vWVYtWrQwyoGMBcW2bdvg6OiIq1evKh1FELSmbt26OHr0KPr166d0lDwxNTXFBx98AACIjo5GXFyc3K6+ePFCyWhCPmm7h2kVgLbZT0iSZApgEQBXANUA9JIkqZokSTUkSdrz2lFay/kEZHYdT5gwAeXLl8eAAQOQnJyMRYsWITo6Gt7e3krHE/KoXr16GDlyJGrUqKF0FEHQGkmS8Omnn0KlKnhzltq3b4/r16+jePHiUKvVaNKkCXr16oVbt24pHU3IA60WTCRPAUh47XRDALdf9RKlAtgEoAPJEJJurx1x73ptSZKGSZIULElSsDGtyJofERER6Ny5MxwdHTF79mw0b94cR44cwY0bN+Dp6SnWTSpgPvroI8yaNcvgZ6rommhL9A9JzJs3D2vXrlU6Sr5lzcROTU2Fm5sbAgMDUa1aNQwdOhR///23wumE3CjRstoBuJ/tcdSrc28kSVJJSZKWAKgjSdL4nM69jmQAyfok69vY2GgwfsFFEleuXMGlS5cAAGZmZvjzzz/x/fffIyIiAjt27MBnn30mllYoYNRqNX788UfR2GqJaEv0jyRJ2LZtGw4fPqx0lHdmaWmJGTNmICIiAsOHD8eaNWtQsWJF9OjRA0FBQUrHE95A7/s0ST4G8PXbzgk5e/78OYoWLQqScHd3R61atbB7926UL18e0dHRYvp5ARcSEgJvb29Uq1YNI7wWpQAAIABJREFUjo6OSscRBJ04cuQIihQponSM91amTBn89ttv+P7777Fw4UL4+/tjy5YtaNGiBb777ju4ubmJXmM9ocT/C9EAsi/UY//qnKBBz549w/Lly+Hi4gJnZ2ekp6fDxMQEW7duxapVq+TniWKp4KtVqxYiIiLQvXt3paMIgs5kFUuGsjSOvb09Zs+ejfv378PHxweRkZHw8vKSF+k0lH9nQaZEwXQBgLMkSY6SJJkD6AkgUIEcBic1NRWBgYHo3r07ypQpgyFDhiA6Ohqenp54+fIlgMyF30qWLKlwUkFTUlJSAADlypUTMxgFo7NkyRLUq1dPr1b+fl9WVlYYNWoU7ty5g8OHD0OlUuHly5eoXbs2NmzYoHQ8o6bVW3KSJG0E8AmAUpIkRQH4ieRySZJGADgIwBTACpI3tJnD0P39999YunQpli9fjri4ONjY2GDYsGHo27cvGjRoIMYkGSi1Wo2mTZuidevWmDNnjtJxBEHnbGxsUKVKFSQmJur1IpbvQqVSoVKlSgCAhIQEfPjhh8gaQxcfH4+MjAyUKVNGyYhGR6sFE8leOZzfB2CfNq9tLMLCwlCtWjVIkgQ3NzcMHToUbdq0EbfajEBaWhrat2+PmjVrKh1FEBTRpUsXdOnSRekYWmdra4vAwP+/EfPzzz/D398fnp6e+P7770XhpCN6P+hb+C9vb28kJSVh2rRpqFy5Mn777Td07NhR7OFmZCwsLDB9+nSlYwiC4h48eABra2uYm5srHUUnPDw8kJCQAB8fH/j5+cHDwwPff/89ypYtq3Q0gyaG3hcAarUaf/75p/w4PDwcN27ckPd58/LyEsWSkTl9+jTOnj2rdAxBUFxQUBDs7Oywb5/x3LSoVKkSVq9ejbCwMHTr1g2//vornJycMGbMGHmDdEHzRMGkxx48eABvb29UqlQJLVq0QNamn/7+/vj999/F2CQjNnXqVHz55ZfIyMhQOoogKKpu3br46aefUKtWLaWj6Jyzs7NcOHXv3h2//vorHB0dMXr0aMTFvfO6z0IORMGkZ+Lj4+Hv749PP/0U5cqVw9ixY2Fvb48NGzbIW16I2VDC9u3bsWPHDvGzIBg9lUqFyZMnG/UaZM7Ozli1ahXCwsLQo0cPLFiwAFmr0iclJYklCTREMoZvZP369ZnVO6OPUlNTsWHDBmzatAlHjhxBRkYGqlSpgh49eqBnz56oUqWK0hEFPZH1+yp6F/9NkqSLJOtr+zr63pYYK5IICgoCSTRu3FjpOIqLiYlBuXLlAAC9evXC/fv38ccff4h2Iw9ya0tED5NCnj9/jitXrgAATExMMHbsWNy6dQtjx47FlStXcPPmTUyZMkUUS8K/7NmzB82aNUN0tFjrVRCy69OnD6ZOnap0DL2QVSwBQLt27dC9e3dIkgSSmDp1KkJDQxVMV3CJWXI6lDVIGwD69u2Ly5cv4+7du1CpVLh48SLs7e3FJwAhVxkZGbC0tETp0qWVjiIIeiNrbzknJyelo+idfv36yf8dGhqKmTNnYsqUKfj0008xfPhwdOzYUWy9kkfiu6QDL168gK+vL5ydnREVFQUAGD9+PNavXy8/p3z58qJYEt6qY8eOOHbsmFhnSxBeU7t2bRQrVkzpGHqtWrVquH//PmbOnInbt2+jS5cuaNKkCS5evKh0tAJBFExalJSUBG9vbzg6OsLLywu2trZ4+vQpgMwtSpo3by6KJCFPSOLgwYMGtQWEIGjaoUOH4OXlpXQMvVa6dGmMHz8eERERWLNmDSIjI9GgQQMMHz4cT548UTqeXhMFkxY8ffoU06dPR4UKFTB27FjUrFkTJ0+exB9//IGPP/5Y6XhCAXT06FG0bdsWW7ZsUTqKIOit0NBQ7Nq1CwkJCUpH0Xumpqbo168fwsPD4eXlhSVLlqBy5crY9H/t3Xlc1HX+B/DXe7iUU0BERRAPlNPb8t7ItLS8bTdd0fIoNVNz17PfepaZx+qa21qZtVCeaZp5VK7n5pGiIUpI4oUcAiogAiPDvH9/zMx3geSeYWB4Px+PeTDfc96fz8x8eM/n+/l+v9u2mTu0GksSJiNKS0vDggUL4OPjg4ULF6Jnz544c+YMfvjhB/Tp08fc4YlaLDQ0FDt37sTw4cPNHYoQNdbkyZNx8+ZNuLm5mTuUWsPFxQX/+Mc/cOHCBfj5+SEzM9PcIdVYMujbiGbPno3w8HC8/PLLWLBgQZ28kJowrvv37yMjIwMtW7bEyJEjzR2OEDWanZ0dAN2lWq5cuYKOHTuaOaLao3379jh58qQyvWnTJly6dAmrVq1S6rWukx6mKkhPT8eUKVNw6dIlAMCiRYsQExOD7du3S7IkjGLs2LHo27cv1Gq1uUMRotaYNm0aQkNDZUxOBalUKuWMuevXryMmJka5P19+fr45Q6sRpIepArRaLc6ePYu8vDyEhoZi/vz52Lx5Mzp06IB27drV6SvNCtP44IMPcOPGDfmFJ0QFzJ8/HwMHDoSrq6u5Q6m1li9fDo1GAyJCUlIS2rdvj1GjRuGNN95AUFCQWWNLTk6Gp6cnVCoVsrOz4eDgUC0nUNX4HiYiaklEnxHR14XmBRDRRiL6moimmPL1DTe+nTlzJnx8fNCjRw+88847AICOHTti/fr1eOONN8DM2LJlCx4/fmzKcEQdkJ+fr9xINCgoCC+99JKZIxKidmnRogWGDh0KAMjKyjJzNLWXtbWuTyUvLw/9+vXDxx9/jODgYPTu3Rtffvkl8vLyqj2m+Ph4BAQEYMOGDQCA119/Hf369aue278ws8keADYDSAVwudj8FwBcBXANwLxy7uvrJ8xTAfiyrG07d+7MFaHRaPjYsWM8bdo0btKkCQNgOzs77tKlCwPgb7755nfbHD16lAFweHh4hV5LiOLWrFnDAPjixYvmDqXWAHCeTdiWcSXbEmFeJ06c4AYNGvDJkyfNHYpFSE1N5ZUrV3Lr1q0ZALu5ufGsWbM4Nja22mLQarW8YMECjo+PZ2bmzZs389///ndleWZmZpX2X1pbYuqEqQ+AToUTJgBWAOIBtARgCyAKQCCAEADfFXs0KrTd18X2PRjAQQCjy4qjIo3cZ599xp6enkqSFBwczLNmzeKsrCzOy8vjrVu38uPHj3+3nVar5f/85z+cn5/PzLoEKjIystyvK4SBWq3mPXv2mDuMWkUSJvEkWVlZHBYWxrdu3TJ3KBaloKCADx8+zCNHjmRra2sGwM8//zwXFBSY5PWioqL4mWee4dTU1FLXO3XqFDs7O/OJEycq/VqltSUmPSTHzCcAFL8gxlMArjHzdWZ+DGAbgCHMHM3MLxV7pJay72+ZeQCAPz9pORG9TkTniei84a7N5dGwYUP06tULO3bsQGpqKpgZarUaTk5OsLOzwyuvvPLEqywTEZ599lmlC3PevHl47bXXDMmdEKViZmzatAnZ2dmwtbXFkCFDzB2S0KtsWyLMz8nJCeHh4fDx8TF3KBZFpVKhb9++2Llzp3Ll8KCgIJPdYoWZkZCQgISEhFLX8/T0xPDhw5WzIzMzM437P7ikTMpYDwC+KNrDNBLApkLTYQA2lLK9O4CN0PVKzdfPewbAegAfA3izrBgq8qtw9erV3KpVK6UXqbLdexkZGRwTE8PMzHl5ebx69WrOzs6u1L5Kk5mZyZ9++ilfvXqVmZkvXbrEjRs35h9//JGZmRMTE3n9+vV8584dZtb9MtBqtUaPQ1TNpUuXWKVS8Zo1a8wdSq0E6WESpcjJyeFx48bxZ599Zu5QarXs7GyOjIxUepK2bNnC3bp1Y41Gw8zM+/bt4+XLl7Nara7ya6WkpBQZ4mI4elNeBQUF3K1bNw4LC6vQdqW1JTV+0Dcz32Pmyczcipnf1887xszTmfkNZv6nMV8vJCQEAwcORE5ODgBU+t5ELi4uCAgIAAAcOnQIf/3rX3H69GkAQEpKCpKTkyuV+ebn52PHjh04c+YMAN196iZNmoTvvvsOAFCvXj0MHDgQXl5eAICLFy9i+vTpSmZ+8OBBODs745dffgGgu87PzZs3K1VGYTwhISE4ffo0Zs6cae5QhLA4tra2SEpKQmpqiQctxBMkJydj3rx5MPSsRkREoHPnzkhMTASgGxTu5OSkXOzyyJEj+OSTT5SjMNu3b8eePXvK/XparVa5fMGKFSswefJk3L17V3mtimBmjBo1CgMHDqzQdmXu1JQP/L6HqTuA7wtNz4e+58hUj5rwqzA6Olp5Pn36dHZ0dFR6ej766CN+6623lOXXrl3jmzdvKtM//vgjHzp0iJl1WbO7uztPnDixyPol9RpptVq+e/eukvH/8ssvPGPGDE5LS2Nm5uXLl7NKpVJ6oET1Cg8P5//+97/mDqPWg/QwiTIYekFE+R0+fJitrKyU8bg3btzgXbt28cOHD0vcpvCRlG7dunG/fv2U6a1btyr/C3Nzc/nAgQMcFxfHzMyxsbFsb2/P27dvV/Zz5coVo5epLKW1JeZImKwBXAfQAv8b9B1kyhhqWiP3888/81dffaVMz5kzh0NDQ5XpYcOGcUBAgDLdvXt37tWrlzIdFxdX4e7Jkty+fbtIN/WCBQt44cKFRtm3KJ1areaAgAAeOnSouUOp9SRhEuUVGRlZ5Kwq8T/5+fk8ceJEXrVqFTPrfnDfvn27SvtLTk5mZl175+DgwNOmTWNm3XASAPzee+8xsy6BmjFjBp8/f76Kpaia0toSk164koi2QjfeqCER3QGwiJk/I6JpAL6H7oy5zcx8xZRx1DRdu3ZF165dlekPPvigyPJ58+YVuUJtREQEmjRpokz7+fkZLRZvb2+MHz9emU5MTCwyqP3w4cPo2bMn6tevb7TXrOsKCgqQk5MDJycnHDt2DA4ODuYOSYg6Y/Pmzdi7dy8mTJhQ6SEXlubBgwdwdXWFtbU17t27pxxiIyJ4e3tXer/W1tZo3LgxAN1h0fj4eOWQm7OzM06fPg1/f38AuuEk69atq2JJTIt0CZVl69KlC58/f97cYdQazAwiwu3bt+Hr64slS5bgb3/72+/W02g0yM3NhYODg3LF1bS0NHh7e8Pa2hrp6emwtbWVRqkQjUaDTp06oWfPnvjXv/5l7nAsBhFFMnMXU7+OtCW1X25uLnJycuDu7o6cnBykp6db1Fl0zIyrV6/Cw8MD7u7u0Gg0SEtLg6urK+rVq6f0lhjOaPvnP/+JBQsWID4+Hg0bNlTa/7qqtLakxg/6FtXP8GVp1qwZDh8+jAkTJgAAfvrpJ9ja2iImJgYAsG3bNjg7O+P69esAdAP8WrZsiaSkJADAzp074erqilu3bgHQDSBMT0+v7uKYXW5uLg4dOgRA94srLCwML7zwgpmjEqJuql+/Ptzd3QHoevcDAwOVNqu2ys/PR0ZGBgAgNjYWAQEB+OabbwAAt2/fRtOmTbFjxw5luZWVFbZv3w4ACA0NxZQpU2BlZQUAdTpZKoskTKJEKpUKzz77LJo2bQoAUKvVmDVrlnJ/pk6dOmH16tVwc3MDAPTp0weff/65srx///5YtmyZ8utt9erV8Pb2Vm4fExsbq5xtURm5ubkoKCio9PbVZeXKlRg4cKByNuLs2bPlOktC1ADjx4/H+++/r7RxVWmPqqKgoKDCN9g2HB3Kz8+Hj48PlixZAgDw9/fHl19+iX79+gEA3N3dsXHjRnTr1k2ZXrRokXI/uMDAQKxYsULuu1ceJQ1usqSHDNSsGX755Zci19V48cUXuW3btsr0sWPH+KefflKmlyxZwl988YUy/dxzz/GiRYuUaRcXF54yZYoyHRQUxMuWLVOmhwwZUmT7+fPn86lTp4xWnpJkZWXxkiVL+Ny5c8ysu53AsWPH5PpXJgQZ9C2q6NatW2xvb8//+Mc/jL7vAwcOcFhYmHKyzkcffcRt27ZV2oS5c+cyESln8n344Yfcv39/ZfuDBw8WiWvy5Mk8YsQIZXrt2rV8+PBho8ddF5XWlkgPk6g27du3R1hYmDL93nvvKTdQBICJEydi9erVyvS3336LU6dOKdPNmzeHh4dHke0NN9gEgB49eqBVq1YAdD8E7t69i0ePHgHQ/Qpbs2aNsr+8vDzMnj0bV64Y73wDLjQecP369fjxxx8BAB4eHvjDH/4gXd1C1GAeHh6YM2dOkZv2ajSaSu0rMjISAwYMUK5fdPv2bZw8eRK5ubkAgEaNGqFjx47KAOgXX3wRK1euVA6LqVQq2NraKvvbvXs3VqxYoUz7+vqidevWyvTMmTPRt2/fSsUqyk8GfYsa47fffoO9vb1y0U1jU6vVyM/Ph6OjIy5cuIDu3btj9+7dePHFF3H9+nVs2rQJU6dORbNmzZ64PRcaDHn27FnExsZi3LhxAIC//e1vOHPmDH744QcQEe7fv68cqhSmJ4O+hbGNGTMGSUlJOHLkCADg+PHjcHJyQqdOnX63rlqtxrfffot27dqhbdu2iIqKwrBhw7B161Y8/fTTVY6FmfHo0SM4OjpWeV+idDLoW9QKfn5+JkuWAMDOzk5pcDp16oSMjAzlOP/FixexcuVK5OXlAdANcH/77beVXqNly5bBzc1Nmd6+fTumTp2qTDdt2hT+/v7KOARJloSo3YYNG4bQ0FBl+u2338Y777yjTE+YMEG5JExOTg7+/Oc/IyIiAgDQrl07xMfHGyVZAnQDsSVZMj/pYRJC7+HDh3B0dAQRYdWqVVi8eDESExPRoEEDHDp0CMePH8fSpUthY2OjdLU3bNhQDrXVANLDJEwtPj4earUagYGBAICRI0ciMDAQS5cuBQBERUUhODhYOawmaqfS2hJJmIQQtZ4kTEIIY5BDckIIIYQQVSAJkxBCCCFEGSRhEkIIIYQogyRMQgghhBBlkIRJCCGEEKIMkjAJIYQQQpShTlxWgIjSANwC4AIgUz+78PPi0w0BpBvp5Yu/TlXWLW35k5aVVsbi06Yqf0mxVXbdkpaXp/zF59XGz0Bp69Tlz0BzZvZ40srGpG9LHqFqdVOV97ikZeV9X5/0vKrvdXWXp/i04bkxP7+m/h4Wn2dp71FJy4z1HpW3PanMe1RyW1LSTeYs8QHgkyc9f8Iyo93Is/jrVGXd0pY/aVlpZSytPoxZ/uqqg/KU3xI+A1WtA0v+DFTXo6p1U5X3uDLvc1nPa1t5SimH0T6/pv4eWvp7VNIyY71H5W0DqvoeFX/UtUNy+0p4/qRpU7xmVdctbfmTlpVVxtLqw5iqow7KU/7i82rjZ6C0der6Z6C2qMp7XNKy8r6vpni/q7s8xaf3lbBOVZj6e1h8nqW9RyUtq87ylLZeed+jIurEIbmKIqLzXA1XDa6p6nr5AamDul7+0lha3VhaeQDLK5OllQeonWWqaz1M5fWJuQMws7pefkDqoK6XvzSWVjeWVh7A8spkaeUBamGZpIdJCCGEEKIM0sMkhBBCCFEGSZiEEEIIIcogCZMQQgghRBkkYaogInIgovNE9JK5YzEHIgogoo1E9DURTTF3PNWNiIYS0adEtJ2I+ps7HnMgopZE9BkRfW3uWGoaInqGiE7qvyPPmDseY7C0Ns/S2jBLa5NqcvtSZxImItpMRKlEdLnY/BeI6CoRXSOieeXY1VwAO0wTpWkZow6Y+VdmngzgjwB6mjJeYzNS+fcw8yQAkwH8yZTxmoKR6uA6M08wbaTVz0htBAPIBlAPwB1TxVoeltjmWVobZmltkqW3L3XmLDki6gNdQxbOzMH6eVYA4gD0g65xOwdgFAArAO8X28V4AO0BuEPXGKYz83fVE71xGKMOmDmViAYDmAIggpm3VFf8VWWs8uu3WwPgK2a+UE3hG4WR6+BrZh5ZXbGbmpHaiHRm1hKRJ4C/M/Ofqyv+4iyxzbO0NszS2iRLb1+szR1AdWHmE0TkW2z2UwCuMfN1ACCibQCGMPP7AH7X/azvYncAEAggl4gOMLPWlHEbkzHqQL+fbwF8S0T7AdSahMlInwECsALAwdqWLAHG+wxYIiPXzQMAdqaIs7wssc2ztDbM0tokS29f6kzCVAIvAAmFpu8AeLqklZn5HQAgoleh/yVp0uiqR4XqQN+ADofun8EBk0ZWPSpUfgBvAXgOgAsRtWbmjaYMrppU9DPgDuA9AB2JaL6+4bNUFa2b4QCeB9AAwAbThlYpltjmWVobZmltksW0L3U9YaoUZv7C3DGYCzMfA3DMzGGYDTOvB7De3HGYEzPfg268hCiGmXcD2G3uOIzNkto8S2vDLK1NqsntS50Z9F2CRADehaab6efVJXW9Dup6+QGpg9JYWt1YWnkAyyuTlKeGqusJ0zkAfkTUgohsAbwC4Fszx1Td6nod1PXyA1IHpbG0urG08gCWVyYpTw1VZxImItoK4DSAtkR0h4gmMLMGwDQA3wP4FcAOZr5izjhNqa7XQV0vPyB1UBpLqxtLKw9geWWS8tQudeayAkIIIYQQlVVnepiEEEIIISpLEiYhhBBCiDJIwiSEEEIIUQZJmIQQQgghyiAJkxBCCCFEGSRhEkIIIYQogyRMwqyIqAERTdU/b0pEX5vwtToQ0UBT7V8IYRmIyJeIRhea7kJEFnP7EVE5kjAJc2sAYCoAMHMSM4804Wt1ACAJkxB1COlU9H+dLwAlYWLm88w83aiBiVpHEiZhbisAtCKiX4hoJxFdBnR3RyeiPUT0IxHdJKJpRDSLiC4S0RkictOv14qIDhFRJBGdJCJ//fyXiegyEUUR0Qn9JfmXAviT/rX+REQORLSZiH7W73dIodfeS0THiOg3IlpkproRQlSCvofoKhGFA7gMoKDQspFE9IX++RdEtJ6IThHRdSIy/GBbAaC3vq14m4ieIaLv9NssJqJ/69ubW0Q0nIhWElG0vi2y0a/XmYiO69um74moSbVWgjA6SZiEuc0DEM/MHQDMLrYsGMBwAF0BvAcgh5k7Qnfp/bH6dT4B8BYzdwbwVwAf6ecvBPA8M7cHMJiZH+vnbWfmDsy8HcA7AI4w81MAQgGsIiIH/fZPARgBoB2Al4moi7ELLoQwKT8AHzFzEIBHpazXBEAvAC9BlygBunbppL6tWPuEbVoBeBbAYABfAjjKzCEAcgG8qE+aPgQwUt82bYauDRO1mLW5AxCiFEeZ+SGAh0SUCWCffn40gHZE5AigB4CdRGTYxk7/9ycAXxDRDgC7S9h/fwCDieiv+ul6AHz0z39k5nsAQES7oWtQzxunWEKIanCLmc+UY709zKwFEENEnuXc90FmzieiaABWAA7p50dDdzivLXQ/+H7Ut01WAJIrEryoeSRhEjWZutBzbaFpLXSfXRWADH3vVBHMPJmIngbwIoBIIur8hP0TgBHMfLXITN12xW+yKDddFKJ2KdyrVPj7W6/YeoXbGUL5qAGAmbVElM//uymroW0iAFeYuXsF4hU1nBySE+b2EIBTZTZk5iwAN4joZUAZ3Nle/7wVM59l5oUA0gB4P+G1vgfwFul/AhJRx0LL+hGRGxHVBzAUuh4rIUTtdJeIAvSDv4eVY/1Kt0t6VwF4EFF3ACAiGyIKqsL+RA0gCZMwK/1hr5/0g71XVWIXfwYwgYiiAFwBMEQ/f5V+EOZlAKcARAE4CiDQMOgbwDIANgAuEdEV/bTBzwB2AbgEYBczy+E4IWqveQC+g64tKM+hsUsACvQnjbxd0RfTj5kcCeADfdv0C3TDB0QtRv/rSRRCALqz5AB0YeZp5o5FCCFEzSA9TEIIIYQQZZAeJiGEEEKIMkgPkxBCCCFEGSRhEkIIIYQogyRMQgghhBBlkIRJCCGEEKIMcqVvUaNERkY2sra23gTdbQUkoRdCiJJpAVzWaDQTO3funGruYCydJEyiRrG2tt7UuHHjAA8PjwcqlUpO4RRCiBJotVpKS0sLTElJ2QTdjYCFCckveFHTBHt4eGRJsiSEEKVTqVTs4eGRCV2PvDAxSZhETaOSZEkIIcpH317K//JqIJUsRDH29vYdi8+bNWtW00aNGrXz9/cPNDzS09OtDMvHjx/v3ahRo3YFBQXKNuvXr3d3dXVt7+/vH9iqVaugNWvWNCw+39/fP3DYsGG+ADBixAhfLy+vEH9//8C2bdsG7t27V7n5Z15eHo0fP97bx8cnuHnz5sF9+/ZtFR8fb2NYnpCQYD1o0KAWzZo1CwkKCgro0KGDf3h4eAPT1FD1mjBhgvfSpUsbGaZ79erl96c//am5YXrSpEnNFi9e7Onn51fk5qazZs1qunDhQs/qjNVUjFUHCxcu9GzRokWQv79/YHBwcMCGDRvcq6cEQtR+kjAJUU6TJ0++GxsbG2N4NGzYsAAACgoKcOjQoQZNmjR5fODAgSJ3OB80aNCD2NjYmBMnTlx99913vRISEqwLz4+NjY355ptvbhrWf/fdd+/ExsbGrF69OmH69OnKP8Tp06d7ZWdnq65fv3751q1blwcPHpwxdOjQ1lqtFlqtFoMGDWrdu3fv7Dt37kRfuXLl1x07dlxPSEiwraaqMalevXplnzlzxhHQ1fWDBw+sr169Wt+w/Ny5c469e/fONl+EpmeMOli5cqXHkSNHnCMjI381fCYt7U4Pc+fObdy6deugNm3aBPr7+wceOXLEAQCSk5Otra2tO61cudKj8PpeXl4hhnXbtGkT+OWXXxb5kREREdGAiDpfvHixXuH5t27dsgkNDW0NAGq1moYPH+7bpk2bwJYtWwbNnz+/8ZNiy8vLo1GjRjX39fUNbtGiRdAXX3xR4g+a48eP21tbW3f+/PPPXQEgKSnJunfv3n6VqxVhLJIwCVFF+/fvd/Lz88udOHFi2pYtW9yetI6Xl5fGx8dHfe3atXIlMX379s1OTU21AYCHDx+qduzY0XDjxo0J1ta68zRmzJhxz9bWVrtv3z6nffv2OdnY2PCcOXPSDNu3adPm8TvvvGMRZ82EhoZmX7hwwREAIiMj67dt2zbXwcGhIC0tzSrwoq2mAAAK00lEQVQ3N5fi4+PreXh4aMwdpykZow7Wrl3b+JNPPrnl5uamBQA3NzftW2+9da864q8Ohw8fdvj+++8bREdHx8TFxcUcPXo0rmXLlo8BIDw83LV9+/aPdu7c+bvv5/Hjx+NiY2Njdu7cGT9nzhzvwsu2bdvm1qlTp+zw8PAi2y1fvtxzwoQJ6QDw+eefuz5+/FgVFxcXExUV9Wt4eLjH1atXf/c9nz9/fhMPD4/8mzdvXr527dqV559//okJrkajwdy5c5v17Nkz0zCvadOmGk9Pz/wffvjBoXK1I4xBzpITNdpTTz3Vtvi84cOH3583b17aw4cPVX379v3dr64xY8akT58+/V5ycrL1kCFDWhVe9vPPP1+tbCwbN2703LFjhzsAuLi4aM6ePRsHAFu2bHH74x//eH/UqFEZy5Yt81Kr1WRnZ1fkp3tMTIxtQkKCXWBgoDo6Orr+vn37XP39/R0BYMqUKXdnzJhR5B/Xrl27XJ577rkM/bZ2TZo0eWz4R2fQoUOHnOjo6PoA0K5du5zKlqu8xo8f73358mV7Y+4zODg4Z/PmzQmlrePr65tvZWXFv/32m+3x48cdunXr9igxMdHmyJEjjq6urpo2bdrk2tnZcUJCgp2/v3+gYbv09HSbqVOnphgzXoMnfS6Le+GFFzKWLl1617B+VT6XVa2D+/fvqx49emQVGBj4uLJlrojC5VWr1dS7d+82r776atrUqVPvG763kyZNSp00adKDe/fuWQ0YMKD1m2++eXfcuHEZhvqZOXNmyujRozNv375t7ePjU2ZCnJiYaOPm5qapX78+A0CTJk2UbXbu3Om2evXqhHHjxrWMj4+3adWqVX7x7TMyMqycnZ2VY+qZmZmqc+fOOR4+fPjq4MGD/dauXZtkWLZ//37XdevWJQIAESEnJ0eVn5+PR48ekY2NDTdo0KCg+P63bt3aMC4u7jIAWFlZFYmvsOXLlzcaMmTIg/PnzxdJjoYOHZoRHh7u3r9//0dl1YUwDelhEqKcCh+SMyRLeXl5dOTIEZfRo0dnuLm5aTt06PBo9+7dzoZt9IlR4CuvvNJy3bp1tzw9PQuAoofkCidL//d//9fM19c3+PXXX2+xYMGCSv2zDwsL82nbtm1gcHBwQFXLXFN07tw5++jRow6nT5927N27d3aPHj0e/fTTTw4nT550fPrpp7MBwNvbW134kOnYsWPTytpvbSJ1ULqhQ4dmJSUl2fr6+gaPGTPGZ//+/Y4AcO3aNZu0tDSb0NDQnMGDBz8o3lv0hz/8oY2fn1/QCy+80HbRokWJhvlbtmxp8Mwzz2S2a9dO7erqqjl58qQ9AMTGxtq6uLgoidmrr776wN7eXtuoUaP2LVq0aDdt2rQUw/fcwDDecdasWU0DAwMDBgwY0NJweL6wGzdu2Ozbt8+1cG+xQc+ePR/9/PPPjsaoK1E50sMkarTSfnk7OTlpS1vepEkTTVV6lMpj9+7dzg8fPrQKDg4OAoDc3FxVvXr1tKNGjcoEdIlReHj47fLu7913373z2muvPXjvvfcaTZw40ffKlSu/BgQEqJOTk20fPHigcnV1VXqZoqKi7AcPHpwBAHv37nU1zI+IiLidnJxs3aVLF6MmTGX1BJlSjx49sk+dOuUYGxtbv2vXrrktW7Z8vG7dOk9HR8eCV199Nb2646no56rw+pX9XFalDtzc3LT29vbamJgY2+roZSpcPjs7Oy48Xfx76+7uXlBa/ZSndwkAXFxctJcvX445dOiQ03/+8x+ncePGtVq4cOGd9PR068GDBz8AgLCwsPsTJkzwXbJkyV3DdsePH49r0qSJ5sqVK3b9+/dvM3DgwCsuLi7aHTt2uE2fPj0VAEaMGHE/IiLCrXfv3jkJCQk2bm5umkLb26tUKk5JSbmUnp5u1bNnT/+BAwdmFa7n/Px8unv3rk3Pnj0fbdq06c7ixYs933rrLe89e/bcKFyGqVOneq9YseKOlZUVimvatKkmNTXVIsYl1lbSwyREFWzdutVt3bp1txITE6MTExOjb968Gf3f//7X+eHDh1X6bs2fPz9Vq9XSrl27nJ2dnbUjR45MnzJlirdGo2unN2zY4J6Xl6caNGjQw0GDBj1Uq9X0wQcfKANas7OzLeq73adPn+zDhw83aNCgQYG1tTU8PT0LsrKyrC5evOj47LPP1olDFFWtg5kzZyZPnjy5+f3791WA7pCTpZ0lZ21tjZdeeunh2rVrk1atWnV7z549rrt27XLbvn27u5eXV8jw4cNbX716tX50dLRd8W2DgoLU7u7u+RcuXKh39+5dqzNnzji9+eabzb28vEI2bNjQeN++fa5arRb29vZatVqtfL8iIiLcn3/++Uw7Ozv28vLSdO3aNfvUqVNFDqd5enpq6tWrpx07duwDABgzZsz9Jx3evnTpksPYsWNbenl5hRw8eND1L3/5i09EREQDAMjJySE7Oztt8W1E9bGoRlUIY8jLy1N5enq2MzwWL17sCejGMBW+rEBkZGS9EydOuLz88ssZhm2dnZ21Xbp0yd62bZtLVWJQqVSYO3du0urVqxsDwIcffphoZ2enbdGiRXDz5s2Dd+/e7bpnz55rKpUKKpUK+/btiz958qSTl5dXSEhISMCYMWN8Fy9efKdqNVFzPPXUU7kZGRnWXbp0UQbK+vv75zo6OhaUNBbE0lS1DubMmZPWp0+frE6dOgX6+fkFdevWzd+SrnkWFRVlVzgRunjxYv2CggI8evTIKjU19ZLhR820adNS/v3vf/9u8HdiYqL1nTt37Fq3bv04IiLCddiwYfeTkpKiExMTo1NSUi41a9bs8ffff+8YEhKiTkxMVHp6fHx8Hh89etQZALKyslQXLlxwCAkJyQOA7t27t7lx44aNSqVC3759M/fv3+8EAAcOHHD28/PLBYDw8PAGb775ppc+hmjDY8CAAQ/WrFlzOywsLAMALl++XK9Nmza5pqxDUTqytNNKRe0WFRV1s3379tV+iEUIUbudPHnSfvr06T5ZWVlWVlZW7Ovrqw4JCcnJzc1VffTRR8rYpLNnz9YfNWpUy+vXr1/x8vIKcXBwKFCpVNBoNDRt2rSUmTNn3nv66afbzJ49O2XkyJFZhu3efffdRr/++mu9r7766nb37t3bfPrpp7eCg4PVmZmZqldeecX3t99+q8/MGD16dPqyZcvuFhQUwNvbOyQuLu6yo6Mjx8XF2Y4ePbpFVlaWlbu7uyY8PPymn5/f44ULF3rm5+fT+++/X2TM4ogRI3xfeumlzNdee+0BoLuGlp2dHT/p7NeoqKiG7du39zVh9QpIwiRqGEmYhBA1XXh4eIPz58/br1+/Pqmkdc6dO1fv448/brhp06ZSe3qHDBnS4l//+ldC06ZNS+0l7NKlS9uDBw9e8/Dw+N0ZeJIwVQ8Z9C2EEEJUwNixYzPS09NL/f/ZtWvXvK5du5Z5WHzv3r03ylonKSnJesaMGXeflCyJ6iM9TKJGkR4mIYSoGOlhqh4y6FvUNFqtVkvmDkIIIWoDfXspZ89VA0mYRE1zOS0tzUWSJiGEKJ1Wq6W0tDQXAJfNHUtdIGOYRI2i0WgmpqSkbEpJSQmGJPRCCFEaLYDLGo1morkDqQtkDJMQQgghRBnkF7wQQgghRBkkYRJCCCGEKIMkTEIIIYQQZZCESQghhBCiDJIwCSGEEEKU4f8BQkQs4ajsXM0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
    "plt.tight_layout()\n",
    "for _ax in ax:\n",
    "    _ax.set_xscale(\"log\")\n",
    "    _ax.set_yscale(\"log\")\n",
    "ax[0].set_xlabel(\"timestep\");\n",
    "ax[1].set_xlabel(\"runtime\");\n",
    "ax[0].set_ylabel(\"error\")\n",
    "\n",
    "for m, method in enumerate(methods):\n",
    "    ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
    "    ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
    "\n",
    "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**EOS with $\\Phi_0=\\Phi_1=LF$**\n",
    "\n",
    "We now run several EOS methods where we set both the inner and outer operator splitting method to the standard second order leapfrog method. Our resulting EOS method will therefore also be a second order method. We vary the number of steps $n$ taken by $\\Phi_1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ns = [1,2,4,8,16]\n",
    "results_lf = np.zeros((len(dts), len(ns), 2))\n",
    "for i, dt in enumerate(dts):\n",
    "    for j, n in enumerate(ns):\n",
    "        sim = initial_conditions()\n",
    "        sim.dt = dt\n",
    "        sim.integrator = \"eos\"\n",
    "        sim.ri_eos.phi0 = \"lf\"\n",
    "        sim.ri_eos.phi1 = \"lf\"\n",
    "        sim.ri_eos.n = n\n",
    "        sim.ri_eos.safe_mode = 0\n",
    "        results_lf[i,j] = run(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the following plot that for $n=1$, we recover the LEAPFROG method. For $n=16$ both the accuracy and efficiency of our EOS method is very similar to the standard WH method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
    "plt.tight_layout()\n",
    "for _ax in ax:\n",
    "    _ax.set_xscale(\"log\")\n",
    "    _ax.set_yscale(\"log\")\n",
    "ax[0].set_xlabel(\"timestep\");\n",
    "ax[1].set_xlabel(\"runtime\");\n",
    "ax[0].set_ylabel(\"error\")\n",
    "colors = plt.cm.viridis(np.linspace(0,1,len(ns)))\n",
    "\n",
    "for j, n in enumerate(ns):\n",
    "    label = \"$\\Phi_0=\\Phi_1=LF$, $n=%d$\"%n\n",
    "    ax[0].plot(dts/np.pi/2.,results_lf[:,j,0],label=label,color=colors[j])\n",
    "    ax[1].plot(results_lf[:,j,1],results_lf[:,j,0],label=label,color=colors[j])\n",
    "\n",
    "for m, method in enumerate(methods):\n",
    "    ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
    "    ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m]) \n",
    "\n",
    "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**An extra factor of $\\epsilon$**\n",
    "\n",
    "We now create EOS methods which are comparable to the Wisdom-Holman method with symplectic correctors. For the same timestep, the error is smaller by a factor of the mass ratio of the planet to the star, $\\epsilon$. We set $\\Phi_1$ to the fourth order LF4 method and use $n=2$. For $\\Phi_0$ we try out LF4, LF(4,2) and PMLF4. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi0s = [\"LF4\", \"LF4_2\", \"PMLF4\"]\n",
    "results_4 = np.zeros((len(dts), len(phi0s), 2))\n",
    "for i, dt in enumerate(dts):\n",
    "    for j, phi0 in enumerate(phi0s):\n",
    "        sim = initial_conditions()\n",
    "        sim.dt = dt\n",
    "        sim.integrator = \"eos\"\n",
    "        sim.ri_eos.phi0 = phi0\n",
    "        sim.ri_eos.phi1 = \"LF4\"\n",
    "        sim.ri_eos.n = 2\n",
    "        sim.ri_eos.safe_mode = 0\n",
    "        results_4[i,j] = run(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the following plot that the EOS methods using LF(4,2) and PMLF4 do approach the accuracy and efficiency of the Wisdom-Holman method with symplectic correctors for small enough timesteps. To achieve a better accuracy for larger timesteps, we could increase the order of $\\Phi_1$ or the number of steps $n$. Note that the EOS method with $\\Phi_0=LF4$ is a true 4th order method, whereas the methods with LF(4,2) and PMLF4 have generalized order (4,2). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
    "plt.tight_layout()\n",
    "for _ax in ax:\n",
    "    _ax.set_xscale(\"log\")\n",
    "    _ax.set_yscale(\"log\")\n",
    "ax[0].set_xlabel(\"timestep\");\n",
    "ax[1].set_xlabel(\"runtime\");\n",
    "ax[0].set_ylabel(\"error\")\n",
    "\n",
    "for j, phi0 in enumerate(phi0s):\n",
    "    label = \"$\\Phi_0=%s, \\Phi_1=LF4, n=2$\" % labels[phi0]\n",
    "    ax[0].plot(dts/np.pi/2.,results_4[:,j,0],label=label)\n",
    "    ax[1].plot(results_4[:,j,1],results_4[:,j,0],label=label)\n",
    "\n",
    "for m, method in enumerate(methods):\n",
    "    ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
    "    ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m])   \n",
    "    \n",
    "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**High order methods**\n",
    "\n",
    "Next, we will construct arbitrarily high order methods using LF, LF4, LF6, and LF8 for both $\\Phi_0$ and $\\Phi_1$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "phis = [\"LF\", \"LF4\", \"LF6\", \"LF8\"]\n",
    "results_2468 = np.zeros((len(dts), len(phis), 2))\n",
    "for i, dt in enumerate(dts):\n",
    "    for j, phi in enumerate(phis):\n",
    "        sim = initial_conditions()\n",
    "        sim.dt = dt\n",
    "        sim.integrator = \"eos\"\n",
    "        sim.ri_eos.phi0 = phi\n",
    "        sim.ri_eos.phi1 = phi\n",
    "        sim.ri_eos.n = 1\n",
    "        sim.ri_eos.safe_mode = 0\n",
    "        results_2468[i,j] = run(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plots show that the methods are indeed 2nd, 4th, 6th, and 8th order methods.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
    "plt.tight_layout()\n",
    "for _ax in ax:\n",
    "    _ax.set_xscale(\"log\")\n",
    "    _ax.set_yscale(\"log\")\n",
    "ax[0].set_xlabel(\"timestep\");\n",
    "ax[1].set_xlabel(\"runtime\");\n",
    "ax[0].set_ylabel(\"error\")\n",
    "\n",
    "for j, phi in enumerate(phis):\n",
    "    label = \"$\\Phi_0=\\Phi_1=%s, n=1$\" % labels[phi]\n",
    "    ax[0].plot(dts/np.pi/2.,results_2468[:,j,0],label=label)\n",
    "    ax[1].plot(results_2468[:,j,1],results_2468[:,j,0],label=label)\n",
    "\n",
    "for m, method in enumerate(methods):\n",
    "    ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
    "    ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m])   \n",
    "    \n",
    "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Modified potentials**\n",
    "\n",
    "We can use operator splitting methods which make use of derivatives of the acceleration, or the so called modified potential. For the same order, these methods can have fewer function evaluations, and thus better performance. Let us compare using the sixth order methods LF6 (nine function evaluations) and PMLF6 (three modified function evaluations) for $\\Phi_0$. We keep using LF6 for $\\Phi_1$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "phis_m = [\"LF6\", \"PMLF6\"]\n",
    "results_m = np.zeros((len(dts), len(phis_m), 2))\n",
    "for i, dt in enumerate(dts):\n",
    "    for j, phi in enumerate(phis_m):\n",
    "        sim = initial_conditions()\n",
    "        sim.dt = dt\n",
    "        sim.integrator = \"eos\"\n",
    "        sim.ri_eos.phi0 = phi\n",
    "        sim.ri_eos.phi1 = \"LF6\"\n",
    "        sim.ri_eos.n = 1\n",
    "        sim.ri_eos.safe_mode = 0\n",
    "        results_m[i,j] = run(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following plot, we see that the method using PMLF6 is indeed about a factor of 2 faster than the one using LF6. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
    "plt.tight_layout()\n",
    "for _ax in ax:\n",
    "    _ax.set_xscale(\"log\")\n",
    "    _ax.set_yscale(\"log\")\n",
    "ax[0].set_xlabel(\"timestep\");\n",
    "ax[1].set_xlabel(\"runtime\");\n",
    "ax[0].set_ylabel(\"error\")\n",
    "\n",
    "for j, phi in enumerate(phis_m):\n",
    "    label = \"$\\Phi_0=%s, \\Phi_1=LF6, n=1$\" % labels[phi]\n",
    "    ax[0].plot(dts/np.pi/2.,results_m[:,j,0],label=label)\n",
    "    ax[1].plot(results_m[:,j,1],results_m[:,j,0],label=label)\n",
    "\n",
    "for m, method in enumerate(methods):\n",
    "    ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
    "    ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m])   \n",
    "    \n",
    "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**High order methods for perturbed systems**\n",
    "\n",
    "We can do better than above by making use of high order methods for $\\Phi_0$ which were specifically designed for perturbed systems such as LF(8,6,4) and PLF(7,6,4). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi0s_8 = [\"LF8\", \"LF8_6_4\", \"PLF7_6_4\"]\n",
    "results_8 = np.zeros((len(dts), len(phi0s_8), 2))\n",
    "for i, dt in enumerate(dts):\n",
    "    for j, phi0 in enumerate(phi0s_8):\n",
    "        sim = initial_conditions()\n",
    "        sim.dt = dt\n",
    "        sim.integrator = \"eos\"\n",
    "        sim.ri_eos.phi0 = phi0\n",
    "        sim.ri_eos.phi1 = \"LF8\"\n",
    "        sim.ri_eos.n = 1\n",
    "        sim.ri_eos.safe_mode = 0\n",
    "        results_8[i,j] = run(sim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the following plot that these methods indeed perform very well. With $\\Phi_0=LF(8,6,4)$, $\\Phi_1=LF8$ and $n=1$ we achieve an accuracy and efficiency comparable to SABA(8,6,4). In contrast to SABA(8,6,4) we do not require a Kepler solver. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,2,figsize=(8,3),sharey=True)\n",
    "plt.tight_layout()\n",
    "for _ax in ax:\n",
    "    _ax.set_xscale(\"log\")\n",
    "    _ax.set_yscale(\"log\")\n",
    "ax[0].set_xlabel(\"timestep\");\n",
    "ax[1].set_xlabel(\"runtime\");\n",
    "ax[0].set_ylabel(\"error\")\n",
    "\n",
    "for j, phi0 in enumerate(phi0s_8):\n",
    "    label = \"$\\Phi_0=%s, \\Phi_1=LF8, n=1$\" % labels[phi0]\n",
    "    ax[0].plot(dts/np.pi/2.,results_8[:,j,0],label=label)\n",
    "    ax[1].plot(results_8[:,j,1],results_8[:,j,0],label=label)\n",
    "\n",
    "for m, method in enumerate(methods):\n",
    "    ax[0].plot(dts/np.pi/2.,results[:,m,0],label=method,color=\"black\",ls=linestyles[m])\n",
    "    ax[1].plot(results[:,m,1],results[:,m,0],label=method,color=\"black\",ls=linestyles[m])   \n",
    "    \n",
    "ax[0].legend(loc='upper center', bbox_to_anchor=(1.1, -0.2), ncol=4);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
